Question

A builder set up a wooden frame in which to pour concrete for a foundation to a house. the length of the wooden frame is 24 feet. The width is 32 feet. The diagonal is 40 feet. Which best describes the foundation?

Answer 1

The correct answer is attached below!

Answer 2

The answer is the last option, which is: The foundation may be a rectangle:
`24^(2)+ 32^(2) =40^(2)`

The explanation for this problem is shown below:

1- A rectangle is defined as a parallelogram whose opposite sides are parallel and congruent. Its interior angles are right angles.

2- Keeping the definition above on mind, the diagonal of a rectangle divides it into to right triangles. So, we can verify if the shape of the frame is a rectangle by using the Pythagorean Theorem, which is:

`a^(2)= b^(2) +c^(2)`

Where
`a` is the hypotenuse (the measure of the diagonal) and
`b` and
`c` are the other sides of the right triangle.

3- Therefore, you have that
`a` must be equal to
`40` to conclude that it is a rectangle:

`\\a=\sqrt{24^(2)+32^(2)} \\ a=40`

4-So, as you can see, the answer is the option mentioned before.